Are there OpenAI Gym continuing environments (other than inverted pendulum) and baselines?
I'm not sure why you need a continuing environment, but actually you can make most (if not all) OpenAI Gym environments continuing. When you perform a step, you receive information about the next state, the reward, a termination signal and a dictionary with additional information. Simply ignore the termination signal if you want the episodes to continue indefinitely. In some cases you will need to modify a variable of the environments called $\texttt {_max_episode_steps}$, which may force the simulation to stop or to restart.

About your second question, check a resource called Spinning Up, from OpenAI too. They explain several methods and their implementation.